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Broken symmetries and pattern formation in two-frequency forced Faraday waves | | Jeff Porter
; Mary Silber
; | | Date: |
5 Mar 2002 | | Subject: | Pattern Formation and Solitons | nlin.PS | | Abstract: | We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the effects of time translation, time reversal and Hamiltonian structure for three illustrative examples: hexagons, two-mode superlattices, and two-mode rhomboids. By means of explicit parameter symmetries, we show how the size of various three-wave resonant interactions depends on the frequency ratio m:n and on the relative temporal phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments. | | Source: | arXiv, nlin.PS/0203004 | | Other source: | [GID 779320] pmid12190471 | | Services: | Forum | Review | PDF | Favorites | |
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